Question

g you are playing a game in which you flip 3 fair coins. it costs $1 to play the game, which must be subtracted from your winnings. Calculate the expected value for the game. If all coins show the same (all heads or all tails) you win $7, otherwise you lose your $1. The expected value of the game is

Answer 1

Expected value of the game is $1.75

Explanation:

The probability of getting a head or a tail on flipping a coin is 1/2 and so the probability of winning is 1/2 as we need all heads or all tails . There are 3 fair coins so the expected value of winning is given by =

P(1st coin =x =head)= 1/2

P(2nd coin =x =head)= 1/2

P(3rd coin =x =head)= 1/2

P(1st coin =x =tail)= 1/2

P(2nd coin =x =tail)= 1/2

P(3rd coin =x =tail)= 1/2

E(X= win) = ∑xP(x)= (1/2)³+(1/2)³= 1/8 + 1/8= 2/8

Expected value of winning the game is $ 7*2/8= 14/8=$ 1.75

$ 1.75- $1= $ 0.75

$ 0.75 (8) = $ 6

This means that for a total of $ 8 he gets $ 6.